As a short story i'd suggest that you have a local delivery man type character who acts as an intermediary and provides all his needs... that would be a bit unusual but not grosslyenough to fracture suspension of disbelief. I mean in pay the devil by jack higgins - the daughter of the next house over (who is also the love interest) has left him a food parcel for when he arrives (in that story the protag is an irish american returning to ireland having fought for the south in the american civil war)... not terribly believable but who cares, and thats a novel...
That's what I was going to say. Normally the housekeeper would be making these transactions, or maybe his gentleman's gentleman. He might go round to the haberdasher himself, but if he's that well off, he'll have his suits made in Savile Row in London. If you want him to be visiting the shops in person, you could put it down to him being a "democratic" American, despite his presumably self-made wealth. I take it you want to put him in contact with a certain class of young lady?